In [1]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn import metrics
import statsmodels.api as sm
import os
os.chdir('../Regression Problem') # set your directory in your local machine
In [2]:
os.getcwd()
Out[2]:
'K:\\data\\DataSience\\data_sicence course\\ML\\farzad\\Regression Problem'
In [3]:
data = pd.read_csv('CS_04.csv')
data.shape
Out[3]:
(322, 21)
In [4]:
data.columns
Out[4]:
Index(['Unnamed: 0', 'AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'Years',
       'CAtBat', 'CHits', 'CHmRun', 'CRuns', 'CRBI', 'CWalks', 'League',
       'Division', 'PutOuts', 'Assists', 'Errors', 'Salary', 'NewLeague'],
      dtype='object')
In [5]:
data.head()
Out[5]:
Unnamed: 0 AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits ... CRuns CRBI CWalks League Division PutOuts Assists Errors Salary NewLeague
0 -Andy Allanson 293 66 1 30 29 14 1 293 66 ... 30 29 14 A E 446 33 20 NaN A
1 -Alan Ashby 315 81 7 24 38 39 14 3449 835 ... 321 414 375 N W 632 43 10 475.0 N
2 -Alvin Davis 479 130 18 66 72 76 3 1624 457 ... 224 266 263 A W 880 82 14 480.0 A
3 -Andre Dawson 496 141 20 65 78 37 11 5628 1575 ... 828 838 354 N E 200 11 3 500.0 N
4 -Andres Galarraga 321 87 10 39 42 30 2 396 101 ... 48 46 33 N E 805 40 4 91.5 N

5 rows × 21 columns

In [6]:
data.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 322 entries, 0 to 321
Data columns (total 21 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   Unnamed: 0  322 non-null    object 
 1   AtBat       322 non-null    int64  
 2   Hits        322 non-null    int64  
 3   HmRun       322 non-null    int64  
 4   Runs        322 non-null    int64  
 5   RBI         322 non-null    int64  
 6   Walks       322 non-null    int64  
 7   Years       322 non-null    int64  
 8   CAtBat      322 non-null    int64  
 9   CHits       322 non-null    int64  
 10  CHmRun      322 non-null    int64  
 11  CRuns       322 non-null    int64  
 12  CRBI        322 non-null    int64  
 13  CWalks      322 non-null    int64  
 14  League      322 non-null    object 
 15  Division    322 non-null    object 
 16  PutOuts     322 non-null    int64  
 17  Assists     322 non-null    int64  
 18  Errors      322 non-null    int64  
 19  Salary      263 non-null    float64
 20  NewLeague   322 non-null    object 
dtypes: float64(1), int64(16), object(4)
memory usage: 53.0+ KB
In [7]:
data.isna().sum()
Out[7]:
Unnamed: 0     0
AtBat          0
Hits           0
HmRun          0
Runs           0
RBI            0
Walks          0
Years          0
CAtBat         0
CHits          0
CHmRun         0
CRuns          0
CRBI           0
CWalks         0
League         0
Division       0
PutOuts        0
Assists        0
Errors         0
Salary        59
NewLeague      0
dtype: int64
In [8]:
data.drop(['Unnamed: 0'], axis = 1, inplace = True)
data.head()
Out[8]:
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks League Division PutOuts Assists Errors Salary NewLeague
0 293 66 1 30 29 14 1 293 66 1 30 29 14 A E 446 33 20 NaN A
1 315 81 7 24 38 39 14 3449 835 69 321 414 375 N W 632 43 10 475.0 N
2 479 130 18 66 72 76 3 1624 457 63 224 266 263 A W 880 82 14 480.0 A
3 496 141 20 65 78 37 11 5628 1575 225 828 838 354 N E 200 11 3 500.0 N
4 321 87 10 39 42 30 2 396 101 12 48 46 33 N E 805 40 4 91.5 N
In [9]:
data2 = data.dropna(subset = ['Salary'], axis = 0, inplace = False)
data2.shape
Out[9]:
(263, 20)
In [10]:
data2.describe()
Out[10]:
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks PutOuts Assists Errors Salary
count 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000 263.000000
mean 403.642586 107.828897 11.619772 54.745247 51.486692 41.114068 7.311787 2657.543726 722.186312 69.239544 361.220532 330.418251 260.266160 290.711027 118.760456 8.593156 535.925882
std 147.307209 45.125326 8.757108 25.539816 25.882714 21.718056 4.793616 2286.582929 648.199644 82.197581 331.198571 323.367668 264.055868 279.934575 145.080577 6.606574 451.118681
min 19.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 19.000000 4.000000 0.000000 2.000000 3.000000 1.000000 0.000000 0.000000 0.000000 67.500000
25% 282.500000 71.500000 5.000000 33.500000 30.000000 23.000000 4.000000 842.500000 212.000000 15.000000 105.500000 95.000000 71.000000 113.500000 8.000000 3.000000 190.000000
50% 413.000000 103.000000 9.000000 52.000000 47.000000 37.000000 6.000000 1931.000000 516.000000 40.000000 250.000000 230.000000 174.000000 224.000000 45.000000 7.000000 425.000000
75% 526.000000 141.500000 18.000000 73.000000 71.000000 57.000000 10.000000 3890.500000 1054.000000 92.500000 497.500000 424.500000 328.500000 322.500000 192.000000 13.000000 750.000000
max 687.000000 238.000000 40.000000 130.000000 121.000000 105.000000 24.000000 14053.000000 4256.000000 548.000000 2165.000000 1659.000000 1566.000000 1377.000000 492.000000 32.000000 2460.000000

Histogram Plot for All Features

In [11]:
data2.columns
Out[11]:
Index(['AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'Years', 'CAtBat',
       'CHits', 'CHmRun', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division',
       'PutOuts', 'Assists', 'Errors', 'Salary', 'NewLeague'],
      dtype='object')
In [12]:
var_ind = list(range(13)) + list(range(15, 19))
len(var_ind)
Out[12]:
17
In [13]:
var_ind
Out[13]:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18]
In [14]:
data2.iloc[:, var_ind].info()
<class 'pandas.core.frame.DataFrame'>
Int64Index: 263 entries, 1 to 321
Data columns (total 17 columns):
 #   Column   Non-Null Count  Dtype  
---  ------   --------------  -----  
 0   AtBat    263 non-null    int64  
 1   Hits     263 non-null    int64  
 2   HmRun    263 non-null    int64  
 3   Runs     263 non-null    int64  
 4   RBI      263 non-null    int64  
 5   Walks    263 non-null    int64  
 6   Years    263 non-null    int64  
 7   CAtBat   263 non-null    int64  
 8   CHits    263 non-null    int64  
 9   CHmRun   263 non-null    int64  
 10  CRuns    263 non-null    int64  
 11  CRBI     263 non-null    int64  
 12  CWalks   263 non-null    int64  
 13  PutOuts  263 non-null    int64  
 14  Assists  263 non-null    int64  
 15  Errors   263 non-null    int64  
 16  Salary   263 non-null    float64
dtypes: float64(1), int64(16)
memory usage: 37.0 KB
In [15]:
plot = plt.figure(figsize = (12, 6))
plot.subplots_adjust(hspace = 0.5, wspace = 0.5)
for i in range(1, 18):
    a = plot.add_subplot(3, 6, i)
    a.hist(data2.iloc[:, var_ind[i - 1]], alpha = 0.7)
    a.title.set_text(data2.columns[var_ind[i - 1]])
In [16]:
# Box Plot of Salary
plt.boxplot(data2.Salary, showmeans = True)
plt.title('Boxplot of Salary')
Out[16]:
Text(0.5, 1.0, 'Boxplot of Salary')
In [17]:
cor_table = round(data2.iloc[:, var_ind].corr(method = 'pearson'), 2)
cor_table
Out[17]:
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks PutOuts Assists Errors Salary
AtBat 1.00 0.96 0.56 0.90 0.80 0.62 0.01 0.21 0.23 0.21 0.24 0.22 0.13 0.31 0.34 0.33 0.39
Hits 0.96 1.00 0.53 0.91 0.79 0.59 0.02 0.21 0.24 0.19 0.24 0.22 0.12 0.30 0.30 0.28 0.44
HmRun 0.56 0.53 1.00 0.63 0.85 0.44 0.11 0.22 0.22 0.49 0.26 0.35 0.23 0.25 -0.16 -0.01 0.34
Runs 0.90 0.91 0.63 1.00 0.78 0.70 -0.01 0.17 0.19 0.23 0.24 0.20 0.16 0.27 0.18 0.19 0.42
RBI 0.80 0.79 0.85 0.78 1.00 0.57 0.13 0.28 0.29 0.44 0.31 0.39 0.23 0.31 0.06 0.15 0.45
Walks 0.62 0.59 0.44 0.70 0.57 1.00 0.13 0.27 0.27 0.35 0.33 0.31 0.43 0.28 0.10 0.08 0.44
Years 0.01 0.02 0.11 -0.01 0.13 0.13 1.00 0.92 0.90 0.72 0.88 0.86 0.84 -0.02 -0.09 -0.16 0.40
CAtBat 0.21 0.21 0.22 0.17 0.28 0.27 0.92 1.00 1.00 0.80 0.98 0.95 0.91 0.05 -0.01 -0.07 0.53
CHits 0.23 0.24 0.22 0.19 0.29 0.27 0.90 1.00 1.00 0.79 0.98 0.95 0.89 0.07 -0.01 -0.07 0.55
CHmRun 0.21 0.19 0.49 0.23 0.44 0.35 0.72 0.80 0.79 1.00 0.83 0.93 0.81 0.09 -0.19 -0.17 0.52
CRuns 0.24 0.24 0.26 0.24 0.31 0.33 0.88 0.98 0.98 0.83 1.00 0.95 0.93 0.06 -0.04 -0.09 0.56
CRBI 0.22 0.22 0.35 0.20 0.39 0.31 0.86 0.95 0.95 0.93 0.95 1.00 0.89 0.10 -0.10 -0.12 0.57
CWalks 0.13 0.12 0.23 0.16 0.23 0.43 0.84 0.91 0.89 0.81 0.93 0.89 1.00 0.06 -0.07 -0.13 0.49
PutOuts 0.31 0.30 0.25 0.27 0.31 0.28 -0.02 0.05 0.07 0.09 0.06 0.10 0.06 1.00 -0.04 0.08 0.30
Assists 0.34 0.30 -0.16 0.18 0.06 0.10 -0.09 -0.01 -0.01 -0.19 -0.04 -0.10 -0.07 -0.04 1.00 0.70 0.03
Errors 0.33 0.28 -0.01 0.19 0.15 0.08 -0.16 -0.07 -0.07 -0.17 -0.09 -0.12 -0.13 0.08 0.70 1.00 -0.01
Salary 0.39 0.44 0.34 0.42 0.45 0.44 0.40 0.53 0.55 0.52 0.56 0.57 0.49 0.30 0.03 -0.01 1.00
In [18]:
plt.figure(figsize = (12, 8))
sns.heatmap(cor_table, annot = True)
Out[18]:
<matplotlib.axes._subplots.AxesSubplot at 0x23537bcf148>

Scatter Plot Between Target Value and Features

In [19]:
#Scatter Plot
var_ind = list(range(13)) + list(range(15, 18))
plot = plt.figure(figsize = (12, 12))
plot.subplots_adjust(hspace = 0.8, wspace = 0.5)
for i in range(1, 17):
    a = plot.add_subplot(4, 4, i)
    a.scatter(x = data2.iloc[: , var_ind[i - 1]], y = data2.iloc[: , 18], alpha = 0.5)
    a.title.set_text('Salary vs. ' + data2.columns[var_ind[i - 1]])
In [20]:
targ_x = 'Errors'
targ_y = 'Salary'
print(f'{data2[targ_x].count()} == {data2[targ_x].size} if these numbers are not equal then we have missing value')
print('------------------------------------')
print(f'The min of {targ_x} is: {data2[targ_x].min()}')
print('------------------------------------')
print(f'The max of {targ_x} is: {data2[targ_x].max()}')
print('------------------------------------')
print(f'The quantile of {targ_x} is:\n{data2[targ_x].quantile(q = [.1, .25, .5, .75, .9, .95])}')
print('------------------------------------')
print(f'The mean of {targ_x} is: {data2[targ_x].mean()}')


plt.figure(figsize=(15, 10), dpi = 200)
plt.subplots_adjust(hspace = 0.5, wspace = 0.5)


plt.subplot(221)
sns.boxplot(x = data2[targ_x]);
plt.title(f'boxplot of {targ_x}')

plt.subplot(222)
sns.distplot(data2[targ_x], kde = False);
plt.title(f'Histogram of {targ_x}')


plt.subplot(223)
plt.scatter(x = data2[targ_x], y = data2[targ_y], alpha = 0.5);
plt.title(f'{targ_y} vs {targ_x}')
plt.xlabel(targ_x)
plt.ylabel(targ_y)
plt.subplots_adjust(hspace = 0.5, wspace = 0.5)



plt.subplot(224)
plt.scatter(x = data2[targ_x], y = data2[targ_y]);
plt.title(f'{targ_y} vs log({targ_x})')
plt.xlabel(targ_x)
plt.ylabel(targ_y)
plt.subplots_adjust(hspace = 0.5, wspace = 0.5)
263 == 263 if these numbers are not equal then we have missing value
------------------------------------
The min of Errors is: 0
------------------------------------
The max of Errors is: 32
------------------------------------
The quantile of Errors is:
0.10     2.0
0.25     3.0
0.50     7.0
0.75    13.0
0.90    18.0
0.95    21.9
Name: Errors, dtype: float64
------------------------------------
The mean of Errors is: 8.593155893536121

Categorical Variables

In [21]:
data2['League'].value_counts()
Out[21]:
A    139
N    124
Name: League, dtype: int64
In [22]:
data2['Division'].value_counts()
Out[22]:
W    134
E    129
Name: Division, dtype: int64
In [23]:
data2['NewLeague'].value_counts()
Out[23]:
A    141
N    122
Name: NewLeague, dtype: int64

Data Preparation

In [24]:
from sklearn.model_selection import train_test_split
train, test = train_test_split(data2, test_size = 0.2, random_state = 1234)
print(f'The Shape of train is: {train.shape}')
print(f'The Shape of test is: {test.shape}')
The Shape of train is: (210, 20)
The Shape of test is: (53, 20)
In [25]:
train.describe()
Out[25]:
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks PutOuts Assists Errors Salary
count 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000 210.000000
mean 409.009524 109.923810 11.880952 55.871429 52.290476 41.838095 7.409524 2658.804762 721.333333 70.361905 360.742857 331.709524 259.609524 292.023810 111.880952 8.228571 562.288433
std 148.097730 46.149683 8.872306 25.833802 26.641091 21.846408 4.624038 2126.724958 596.666853 83.085605 307.176493 315.682880 251.547022 275.904453 143.031332 6.307521 466.852811
min 20.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 41.000000 9.000000 0.000000 6.000000 7.000000 4.000000 0.000000 0.000000 0.000000 68.000000
25% 283.000000 73.000000 5.000000 34.000000 30.000000 24.000000 4.000000 928.250000 230.250000 15.000000 116.250000 99.250000 76.500000 110.250000 7.000000 3.000000 210.000000
50% 417.000000 105.500000 9.000000 53.500000 47.000000 37.500000 6.000000 2035.500000 546.500000 40.000000 278.500000 251.500000 179.500000 226.000000 41.500000 6.000000 450.000000
75% 528.750000 144.750000 18.000000 76.000000 73.000000 57.000000 11.000000 3900.250000 1058.000000 92.750000 493.500000 419.750000 318.500000 318.500000 172.250000 12.750000 761.250000
max 687.000000 238.000000 40.000000 130.000000 121.000000 105.000000 20.000000 9528.000000 2583.000000 548.000000 1509.000000 1659.000000 1380.000000 1377.000000 492.000000 29.000000 2460.000000
In [26]:
test.describe()
Out[26]:
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks PutOuts Assists Errors Salary
count 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000 53.000000
mean 382.377358 99.528302 10.584906 50.283019 48.301887 38.245283 6.924528 2652.547170 725.566038 64.792453 363.113208 325.301887 262.867925 285.509434 146.018868 10.037736 431.470491
std 143.530113 40.146177 8.284448 24.056326 22.577716 21.160473 5.445001 2857.368387 828.292045 79.190947 416.452493 355.362414 311.416370 298.059211 151.253797 7.572629 368.025230
min 19.000000 4.000000 0.000000 2.000000 3.000000 1.000000 1.000000 19.000000 4.000000 0.000000 2.000000 3.000000 1.000000 0.000000 0.000000 0.000000 67.500000
25% 278.000000 70.000000 3.000000 32.000000 32.000000 22.000000 3.000000 682.000000 170.000000 16.000000 93.000000 80.000000 50.000000 117.000000 9.000000 4.000000 155.000000
50% 360.000000 103.000000 9.000000 48.000000 47.000000 34.000000 5.000000 1399.000000 357.000000 36.000000 168.000000 154.000000 128.000000 203.000000 80.000000 8.000000 297.500000
75% 511.000000 138.000000 17.000000 68.000000 60.000000 56.000000 10.000000 3828.000000 970.000000 90.000000 575.000000 458.000000 359.000000 325.000000 269.000000 16.000000 670.000000
max 584.000000 163.000000 33.000000 107.000000 104.000000 83.000000 24.000000 14053.000000 4256.000000 384.000000 2165.000000 1314.000000 1566.000000 1320.000000 465.000000 32.000000 1861.460000
In [27]:
final_dataset_train = pd.get_dummies(train,drop_first=True)
final_dataset_train.head()
Out[27]:
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks PutOuts Assists Errors Salary League_N Division_W NewLeague_N
98 415 115 27 97 71 68 3 711 184 45 156 119 99 274 2 7 300.0 1 1 1
206 407 93 8 47 30 30 2 969 230 14 121 69 68 172 317 25 150.0 1 1 1
54 403 101 12 45 53 39 12 5150 1429 166 747 666 526 316 6 5 675.0 0 0 0
177 441 118 28 84 86 68 8 2723 750 126 433 420 309 190 2 2 1300.0 0 0 0
27 474 129 10 50 56 40 10 2331 604 61 246 327 166 732 83 13 750.0 1 1 1
In [28]:
X_train = final_dataset_train.iloc[:, list(range(0,16)) + list(range(17, 20))]
y_train = final_dataset_train.iloc[:, 16]
In [29]:
X_train = sm.add_constant(X_train)
In [30]:
y_train
Out[30]:
98      300.0
206     150.0
54      675.0
177    1300.0
27      750.0
        ...  
183     125.0
192     525.0
256     400.0
72      850.0
263     740.0
Name: Salary, Length: 210, dtype: float64
In [31]:
final_dataset_test = pd.get_dummies(test, drop_first=True)
final_dataset_test.head()
Out[31]:
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks PutOuts Assists Errors Salary League_N Division_W NewLeague_N
295 19 4 1 2 3 1 1 19 4 1 2 3 1 692 70 8 920.0 1 1 0
132 278 70 7 22 37 18 18 7186 2081 190 935 1088 643 0 0 0 325.0 0 1 0
137 343 103 6 48 36 40 15 4338 1193 70 581 421 325 211 56 13 430.0 0 0 0
268 549 149 7 73 47 42 1 549 149 7 73 47 42 255 450 17 140.0 1 1 1
239 309 72 0 33 31 26 5 354 82 0 41 32 26 117 269 12 130.0 1 0 1
In [32]:
X_test = final_dataset_test.iloc[:, list(range(0,16)) + list(range(17, 20))]
y_test = final_dataset_test.iloc[:, 16]
In [33]:
X_test = sm.add_constant(X_test)
In [34]:
y_test
Out[34]:
295     920.000
132     325.000
137     430.000
268     140.000
239     130.000
128     662.500
189    1183.333
209     550.000
276     155.000
236     750.000
227     200.000
320     960.000
215     175.000
178    1000.000
121     200.000
265     140.000
45      305.000
274     200.000
40       67.500
244     215.000
198     145.000
303     425.000
7       100.000
78      325.000
96     1861.460
68      105.000
223     240.000
35      850.000
93      145.000
130     750.000
311     525.000
6        70.000
131     297.500
63      225.000
205      90.000
89      475.000
293     925.000
314     120.000
8        75.000
10      517.143
88      260.000
85      600.000
124     737.500
185     725.000
262     191.000
43      180.000
162      75.000
214     670.000
301     160.000
70      320.000
226     175.000
271    1000.000
195     800.000
Name: Salary, dtype: float64

Bulid Models

Model1: Linear Regression

In [35]:
import statsmodels.api as sm
model1 = sm.OLS(y_train, X_train).fit()
model1.summary()
Out[35]:
OLS Regression Results
Dep. Variable: Salary R-squared: 0.551
Model: OLS Adj. R-squared: 0.506
Method: Least Squares F-statistic: 12.28
Date: Fri, 28 May 2021 Prob (F-statistic): 4.97e-24
Time: 13:50:50 Log-Likelihood: -1504.0
No. Observations: 210 AIC: 3048.
Df Residuals: 190 BIC: 3115.
Df Model: 19
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const 184.2280 107.371 1.716 0.088 -27.565 396.021
AtBat -1.7540 0.751 -2.336 0.021 -3.235 -0.273
Hits 6.5979 2.885 2.287 0.023 0.907 12.289
HmRun 7.3090 7.597 0.962 0.337 -7.675 22.293
Runs -2.7338 3.582 -0.763 0.446 -9.799 4.332
RBI -1.3503 3.172 -0.426 0.671 -7.608 4.908
Walks 5.4445 2.263 2.406 0.017 0.981 9.908
Years -6.5675 14.116 -0.465 0.642 -34.412 21.277
CAtBat -0.2467 0.172 -1.433 0.154 -0.586 0.093
CHits 0.5802 0.895 0.648 0.518 -1.185 2.346
CHmRun 0.0299 2.025 0.015 0.988 -3.965 4.025
CRuns 1.4403 0.886 1.625 0.106 -0.308 3.189
CRBI 0.3874 0.911 0.425 0.671 -1.409 2.184
CWalks -0.6119 0.410 -1.491 0.137 -1.421 0.197
PutOuts 0.2961 0.094 3.141 0.002 0.110 0.482
Assists 0.2956 0.249 1.187 0.237 -0.195 0.787
Errors 0.7347 5.199 0.141 0.888 -9.520 10.990
League_N 5.0153 97.960 0.051 0.959 -188.214 198.245
Division_W -134.5539 47.964 -2.805 0.006 -229.164 -39.944
NewLeague_N 36.0810 98.757 0.365 0.715 -158.719 230.881
Omnibus: 71.108 Durbin-Watson: 1.950
Prob(Omnibus): 0.000 Jarque-Bera (JB): 366.871
Skew: 1.201 Prob(JB): 2.16e-80
Kurtosis: 9.013 Cond. No. 2.17e+04


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.17e+04. This might indicate that there are
strong multicollinearity or other numerical problems.
In [36]:
#Check Assumptions of Regression
#Normality of residuals

#Plot histogram of residuals
sns.distplot(model1.resid, hist = True, 
             kde = True, color = 'green',
             bins = np.linspace(min(model1.resid), max(model1.resid), 30))
Out[36]:
<matplotlib.axes._subplots.AxesSubplot at 0x23538340cc8>
In [37]:
#QQ-plot
qqplot_model1 = sm.qqplot(model1.resid, line = 's')
plt.show()
In [38]:
#Residuals vs. Fitted Values
sns.regplot(x = model1.fittedvalues, y = model1.resid, lowess = True, 
                       scatter_kws = {"color": "black"}, line_kws = {"color": "red"})
plt.xlabel('Fitted Values', fontsize = 12)
plt.ylabel('Residuals', fontsize = 12)
plt.title('Residuals vs. Fitted Values', fontsize = 12)
plt.grid()
In [39]:
#Check Cook's distance
sum(model1.get_influence().summary_frame().cooks_d > 1)
Out[39]:
0
In [40]:
#Check Multicollinearity
#Import library for VIF
from statsmodels.stats.outliers_influence import variance_inflation_factor
def calc_vif(X):
    # Calculating VIF
    vif = pd.DataFrame()
    vif["variables"] = X.columns
    vif["VIF"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]
    return(vif)

calc_vif(X_train.iloc[:, 1:])
#If VIF > 10 then multicollinearity is high
Out[40]:
variables VIF
0 AtBat 184.789083
1 Hits 228.168969
2 HmRun 24.624973
3 Runs 94.783224
4 RBI 67.555583
5 Walks 22.239021
6 Years 19.479370
7 CAtBat 661.537532
8 CHits 1367.185526
9 CHmRun 94.537823
10 CRuns 343.366050
11 CRBI 338.173807
12 CWalks 42.705439
13 PutOuts 2.791098
14 Assists 3.884531
15 Errors 5.490002
16 League_N 8.454530
17 Division_W 2.211985
18 NewLeague_N 8.518855
In [41]:
y_pred_model1 = model1.predict(X_test)
abs_err_model1 = np.abs(y_pred_model1 - y_test)
In [42]:
#Absolute error mean, median, sd, IQR, max, min
from scipy.stats import iqr
model_comp = pd.DataFrame({'Mean of AbsErrors':    abs_err_model1.mean(),
                           'Median of AbsErrors' : abs_err_model1.median(),
                           'SD of AbsErrors' :     abs_err_model1.std(),
                           'IQR of AbsErrors':     iqr(abs_err_model1),
                           'Min of AbsErrors':     abs_err_model1.min(),
                           'Max of AbsErrors':     abs_err_model1.max()}, index = ['Model1: Linear-Ragression'])
model_comp
Out[42]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.57417 198.785517 216.725217 3.569232 1047.957143
In [43]:
y_pred = y_pred_model1
y_test = y_test
model = 'model1_ClassicalRegression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [44]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model1))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model1))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model1)))
MAE: 223.14895772642777
MSE: 88565.56020433208
RMSE: 297.5996643216052
In [45]:
from scipy.stats import boxcox
box_results = boxcox(y_train, alpha = 0.05)
box_results
Out[45]:
(array([ 8.68767642,  7.23164837, 10.57834815, 12.26939869, 10.83994871,
         6.62404411,  7.71258662,  8.68767642, 10.83994871,  8.96581785,
        11.22963399, 12.37152681,  9.42809521, 11.68471715, 11.22963399,
        10.2903865 , 11.07990572, 10.01452882,  6.24460125,  9.33424139,
        12.18523005,  8.49713804,  9.18694201,  9.85379764, 12.05455555,
         6.19217269,  8.29104472,  8.97678487,  9.12564319,  8.58783864,
        10.69755487, 12.26939869,  9.33424139, 13.38038527,  6.62404411,
        14.01171784, 10.66821468, 10.38965872, 11.15571849, 11.30175192,
         9.60648041,  7.84493411,  6.44250966,  7.42366699, 10.08065305,
         8.4167188 ,  7.92100039, 12.83795386,  5.73192967, 10.66821468,
         9.99213228, 11.57398419, 10.34045899, 10.91673547, 12.26939869,
         6.44250966, 11.44095555,  9.60648041, 13.35909851, 11.22963399,
         9.60648041, 13.4314587 ,  9.03092529,  9.7940383 , 10.92754387,
        10.79796189,  6.24460125, 10.44759156, 11.82369329,  9.03092529,
         8.29104472,  6.34580001,  8.15869764,  9.47381214, 10.2083691 ,
         8.26947055,  5.90887785,  7.23164837,  9.24684836, 10.01452882,
        11.0490254 ,  7.92100039,  8.49713804, 11.99844039, 11.41362834,
        10.80640804,  8.68767642, 10.12387788,  7.54348268,  6.17083928,
        11.68053376,  7.81903891,  9.50893969,  8.51684866, 12.56636821,
        11.30175192,  5.78403001, 10.08065305,  6.53513949, 10.38965872,
         9.75754601, 10.18748446,  8.87639431,  6.44250966,  6.44250966,
        10.88954435, 10.66821468, 10.92214468, 10.93830915, 10.78382886,
        11.44095555,  6.02674989,  9.73294395, 12.13686831,  9.85379764,
        13.32103433,  8.06636227, 10.83994871, 11.3952698 ,  7.02231014,
         7.54348268,  9.24684836, 10.83994871,  8.68767642,  9.91228345,
         8.29104472, 10.66821468,  7.65753831,  9.85379764,  9.60648041,
         7.76640072, 10.40910151,  5.78403001,  8.29104472,  7.361395  ,
         6.39468899, 11.30175192,  6.70953284,  7.42366699,  8.11296232,
        13.64505006,  7.2974233 , 10.83994871,  5.78403001, 10.83994871,
        10.27010554,  9.41885521,  7.02231014,  6.24460125,  7.97042109,
         9.11009262,  5.90887785,  8.49713804,  9.33424139,  9.73294395,
        10.2903865 ,  9.12564319,  8.20360216, 10.66821468, 12.65948133,
        10.23940707,  6.7918772 , 11.94128703,  9.60648041, 12.95725001,
        10.92214468,  7.71258662,  6.44250966, 11.15571849,  8.29104472,
         8.68767642, 12.29009183, 10.2903865 ,  9.85379764,  6.27545912,
         8.24770782,  9.80609493,  7.2974233 , 13.16780716,  8.97678487,
        11.70140085, 10.48556693,  7.97042109, 11.22963399, 14.06912423,
         5.90887785,  7.09422321,  8.29104472,  9.47381214,  5.78403001,
        12.09872706,  6.24460125, 11.59559513,  8.51684866,  7.50817102,
         6.62404411,  6.62404411, 10.51185131, 10.80640804,  9.44647459,
         7.05134634,  6.24460125, 10.96238926,  9.03092529, 11.00208722,
         6.8713169 ,  9.96955296,  9.33424139, 11.15571849, 10.80640804]),
 0.13847533404638804,
 (-0.01298332655171587, 0.28931544347094323))
In [47]:
logy_train = np.log(y_train)
In [48]:
import statsmodels.api as sm
model1_box = sm.OLS(logy_train, X_train).fit()
model1_box.summary()
Out[48]:
OLS Regression Results
Dep. Variable: Salary R-squared: 0.569
Model: OLS Adj. R-squared: 0.526
Method: Least Squares F-statistic: 13.22
Date: Fri, 28 May 2021 Prob (F-statistic): 1.28e-25
Time: 13:51:00 Log-Likelihood: -184.45
No. Observations: 210 AIC: 408.9
Df Residuals: 190 BIC: 475.8
Df Model: 19
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const 4.6187 0.200 23.047 0.000 4.223 5.014
AtBat -0.0023 0.001 -1.658 0.099 -0.005 0.000
Hits 0.0128 0.005 2.373 0.019 0.002 0.023
HmRun 0.0191 0.014 1.348 0.179 -0.009 0.047
Runs -0.0045 0.007 -0.671 0.503 -0.018 0.009
RBI -0.0036 0.006 -0.612 0.541 -0.015 0.008
Walks 0.0099 0.004 2.349 0.020 0.002 0.018
Years 0.0535 0.026 2.030 0.044 0.002 0.105
CAtBat 6.129e-05 0.000 0.191 0.849 -0.001 0.001
CHits -0.0003 0.002 -0.171 0.864 -0.004 0.003
CHmRun -0.0009 0.004 -0.243 0.808 -0.008 0.007
CRuns 0.0018 0.002 1.105 0.271 -0.001 0.005
CRBI 9.632e-05 0.002 0.057 0.955 -0.003 0.003
CWalks -0.0012 0.001 -1.529 0.128 -0.003 0.000
PutOuts 0.0003 0.000 1.489 0.138 -8.5e-05 0.001
Assists 0.0004 0.000 0.907 0.366 -0.000 0.001
Errors -0.0048 0.010 -0.496 0.621 -0.024 0.014
League_N 0.1897 0.183 1.038 0.301 -0.171 0.550
Division_W -0.2023 0.090 -2.260 0.025 -0.379 -0.026
NewLeague_N -0.0796 0.184 -0.432 0.666 -0.443 0.284
Omnibus: 12.886 Durbin-Watson: 2.000
Prob(Omnibus): 0.002 Jarque-Bera (JB): 32.178
Skew: 0.099 Prob(JB): 1.03e-07
Kurtosis: 4.907 Cond. No. 2.17e+04


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.17e+04. This might indicate that there are
strong multicollinearity or other numerical problems.
In [49]:
X_train.drop('const', axis = 1, inplace = True)
X_test.drop('const', axis = 1, inplace = True)

Model2: Ridge Regression

In [52]:
from sklearn.linear_model import Ridge, RidgeCV
In [53]:
lambda_grid = 10 ** np.linspace(2, -5, num = 100)
lambda_grid
Out[53]:
array([1.00000000e+02, 8.49753436e+01, 7.22080902e+01, 6.13590727e+01,
       5.21400829e+01, 4.43062146e+01, 3.76493581e+01, 3.19926714e+01,
       2.71858824e+01, 2.31012970e+01, 1.96304065e+01, 1.66810054e+01,
       1.41747416e+01, 1.20450354e+01, 1.02353102e+01, 8.69749003e+00,
       7.39072203e+00, 6.28029144e+00, 5.33669923e+00, 4.53487851e+00,
       3.85352859e+00, 3.27454916e+00, 2.78255940e+00, 2.36448941e+00,
       2.00923300e+00, 1.70735265e+00, 1.45082878e+00, 1.23284674e+00,
       1.04761575e+00, 8.90215085e-01, 7.56463328e-01, 6.42807312e-01,
       5.46227722e-01, 4.64158883e-01, 3.94420606e-01, 3.35160265e-01,
       2.84803587e-01, 2.42012826e-01, 2.05651231e-01, 1.74752840e-01,
       1.48496826e-01, 1.26185688e-01, 1.07226722e-01, 9.11162756e-02,
       7.74263683e-02, 6.57933225e-02, 5.59081018e-02, 4.75081016e-02,
       4.03701726e-02, 3.43046929e-02, 2.91505306e-02, 2.47707636e-02,
       2.10490414e-02, 1.78864953e-02, 1.51991108e-02, 1.29154967e-02,
       1.09749877e-02, 9.32603347e-03, 7.92482898e-03, 6.73415066e-03,
       5.72236766e-03, 4.86260158e-03, 4.13201240e-03, 3.51119173e-03,
       2.98364724e-03, 2.53536449e-03, 2.15443469e-03, 1.83073828e-03,
       1.55567614e-03, 1.32194115e-03, 1.12332403e-03, 9.54548457e-04,
       8.11130831e-04, 6.89261210e-04, 5.85702082e-04, 4.97702356e-04,
       4.22924287e-04, 3.59381366e-04, 3.05385551e-04, 2.59502421e-04,
       2.20513074e-04, 1.87381742e-04, 1.59228279e-04, 1.35304777e-04,
       1.14975700e-04, 9.77009957e-05, 8.30217568e-05, 7.05480231e-05,
       5.99484250e-05, 5.09413801e-05, 4.32876128e-05, 3.67837977e-05,
       3.12571585e-05, 2.65608778e-05, 2.25701972e-05, 1.91791026e-05,
       1.62975083e-05, 1.38488637e-05, 1.17681195e-05, 1.00000000e-05])
In [55]:
lambda_grid = np.linspace(.2, .36, num = 100)
lambda_grid
Out[55]:
array([0.2       , 0.20161616, 0.20323232, 0.20484848, 0.20646465,
       0.20808081, 0.20969697, 0.21131313, 0.21292929, 0.21454545,
       0.21616162, 0.21777778, 0.21939394, 0.2210101 , 0.22262626,
       0.22424242, 0.22585859, 0.22747475, 0.22909091, 0.23070707,
       0.23232323, 0.23393939, 0.23555556, 0.23717172, 0.23878788,
       0.24040404, 0.2420202 , 0.24363636, 0.24525253, 0.24686869,
       0.24848485, 0.25010101, 0.25171717, 0.25333333, 0.25494949,
       0.25656566, 0.25818182, 0.25979798, 0.26141414, 0.2630303 ,
       0.26464646, 0.26626263, 0.26787879, 0.26949495, 0.27111111,
       0.27272727, 0.27434343, 0.2759596 , 0.27757576, 0.27919192,
       0.28080808, 0.28242424, 0.2840404 , 0.28565657, 0.28727273,
       0.28888889, 0.29050505, 0.29212121, 0.29373737, 0.29535354,
       0.2969697 , 0.29858586, 0.30020202, 0.30181818, 0.30343434,
       0.30505051, 0.30666667, 0.30828283, 0.30989899, 0.31151515,
       0.31313131, 0.31474747, 0.31636364, 0.3179798 , 0.31959596,
       0.32121212, 0.32282828, 0.32444444, 0.32606061, 0.32767677,
       0.32929293, 0.33090909, 0.33252525, 0.33414141, 0.33575758,
       0.33737374, 0.3389899 , 0.34060606, 0.34222222, 0.34383838,
       0.34545455, 0.34707071, 0.34868687, 0.35030303, 0.35191919,
       0.35353535, 0.35515152, 0.35676768, 0.35838384, 0.36      ])
In [56]:
ridge_cv = RidgeCV(alphas = lambda_grid, cv = 10, normalize = True)
ridge_cv.fit(X_train, logy_train)
ridge_cv.alpha_
Out[56]:
0.33414141414141413
In [57]:
model2 = Ridge(normalize = True, alpha = ridge_cv.alpha_)
model2.fit(X_train, logy_train)
y_pred_model2 = model2.predict(X_test)
y_pred_model2 = np.exp(y_pred_model2)
abs_err_model2 = np.abs(y_pred_model2 - y_test)
In [58]:
sns.distplot(y_test - y_pred_model2)
Out[58]:
<matplotlib.axes._subplots.AxesSubplot at 0x23539141508>
In [59]:
plt.scatter(y_test , y_pred_model2)
Out[59]:
<matplotlib.collections.PathCollection at 0x2353914b508>
In [60]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model2))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model2))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model2)))
MAE: 226.44167398010137
MSE: 135811.2350773115
RMSE: 368.5257590417683
In [61]:
from sklearn.metrics import r2_score

y_pred = y_pred_model2
y_test = y_test
model = 'model 2 Ridge Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [62]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model2.mean(),
                                             'Median of AbsErrors' : abs_err_model2.median(),
                                             'SD of AbsErrors' :     abs_err_model2.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model2),
                                             'Min of AbsErrors':     abs_err_model2.min(),
                                             'Max of AbsErrors':     abs_err_model2.max()}, index = ['Model2: Ridge Regression']), 
                               ignore_index = False)

model_comp
Out[62]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.57417 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.02955 293.532084 136.707544 7.679097 1897.768941

Model3: Lasso Regression

In [63]:
from sklearn.linear_model import Lasso, LassoCV
In [64]:
lambda_grid = 10 ** np.linspace(2, -5, num = 100)
In [66]:
lambda_grid =  np.linspace(0.0001, 0.01, num = 100)
In [67]:
#K-fold Cross Validation to Choose the Best Model
lassocv = LassoCV(alphas = lambda_grid, cv = 10, normalize = True)
lassocv.fit(X_train, logy_train)
lassocv.alpha_
Out[67]:
0.0015
In [68]:
model3 = Lasso(alpha = lassocv.alpha_, normalize = True)
model3.fit(X_train, logy_train)
y_pred_model3 = model3.predict(X_test)
y_pred_model3 = np.exp(y_pred_model3)
abs_err_model3 = np.abs(y_pred_model3 - y_test)
In [69]:
sns.distplot(y_test - y_pred_model3)
Out[69]:
<matplotlib.axes._subplots.AxesSubplot at 0x2353921fe88>
In [70]:
plt.scatter(y_test , y_pred_model3)
Out[70]:
<matplotlib.collections.PathCollection at 0x235392b5948>
In [72]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model3))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model3))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model3)))
MAE: 294.6218817951447
MSE: 198245.4630943862
RMSE: 445.24764243551726
In [74]:
from sklearn.metrics import r2_score

y_pred = y_pred_model3
y_test = y_test
model = 'model 3 Lasso Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [73]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model3.mean(),
                                             'Median of AbsErrors' : abs_err_model3.median(),
                                             'SD of AbsErrors' :     abs_err_model3.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model3),
                                             'Min of AbsErrors':     abs_err_model3.min(),
                                             'Max of AbsErrors':     abs_err_model3.max()}, index = ['Model3: Lasso Regression']), 
                               ignore_index = False)

model_comp
Out[73]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147

Model4: KNN

In [90]:
from sklearn.neighbors import KNeighborsRegressor
model4 = KNeighborsRegressor(n_neighbors = 2, metric = 'minkowski', p = 2)
model4.fit(X_train, logy_train)
y_pred_model4 = model4.predict(X_test)
y_pred_model4 = np.exp(y_pred_model4)
abs_err_model4 = np.abs(y_pred_model4 - y_test)
In [91]:
sns.distplot(y_test - y_pred_model4)
Out[91]:
<matplotlib.axes._subplots.AxesSubplot at 0x2353f134e48>
In [92]:
plt.scatter(y_test , y_pred_model4)
Out[92]:
<matplotlib.collections.PathCollection at 0x2353f1ffa88>
In [93]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model4))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model4))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model4)))
MAE: 160.4074775800345
MSE: 61439.30636882631
RMSE: 247.8695349752089
In [94]:
from sklearn.metrics import r2_score

y_pred = y_pred_model4
y_test = y_test
model = 'model4 KNN Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [81]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model4.mean(),
                                             'Median of AbsErrors' : abs_err_model4.median(),
                                             'SD of AbsErrors' :     abs_err_model4.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model4),
                                             'Min of AbsErrors':     abs_err_model4.min(),
                                             'Max of AbsErrors':     abs_err_model4.max()}, index = ['Model4: KNN Regression']), 
                               ignore_index = False)

model_comp
Out[81]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
In [82]:
from sklearn.model_selection import cross_val_score
n_neighbors = np.arange(1, 20)
cv = 4
cvscores = np.empty((len(n_neighbors), 2))
counter = -1
for k in n_neighbors:
    counter += 1
    knn = KNeighborsRegressor(n_neighbors = k, metric = 'minkowski', p = 2)
    cvscores[counter, :] = np.array([k, np.mean(cross_val_score(knn, X_train, y_train, cv = cv))])
    
cvscores[np.argmax(cvscores[:, 1]), :]
Out[82]:
array([3.        , 0.40149674])

Model5: Decision Tree

In [100]:
from sklearn.tree import DecisionTreeRegressor
model5 = DecisionTreeRegressor(max_depth = 15, min_samples_leaf = 13, ccp_alpha = 0.0001)
model5.fit(X_train, logy_train)
y_pred_model5 = model5.predict(X_test)
y_pred_model5 = np.exp(y_pred_model5)
abs_err_model5 = np.abs(y_pred_model5 - y_test)
In [96]:
from sklearn.model_selection import RandomizedSearchCV

max_depth = [int(x) for x in np.linspace(1, 20, num = 15)]
min_samples_leaf = np.arange(15)
ccp_alpha = [0.001, 0.01, 0.1, 0.0001]
objective = ['reg:squarederror']

random_grid = {'max_depth': max_depth, 
               'min_samples_leaf': min_samples_leaf, 
               'ccp_alpha': ccp_alpha}

decision = RandomizedSearchCV(estimator = model5, param_distributions = random_grid, scoring = 'neg_mean_squared_error', n_iter = 10, cv = 8, random_state = 40, n_jobs = 1)
decision.fit(X_train, logy_train)
decision.best_params_
Out[96]:
{'min_samples_leaf': 13, 'max_depth': 15, 'ccp_alpha': 0.0001}
In [102]:
sns.distplot(y_test - y_pred_model5)
Out[102]:
<matplotlib.axes._subplots.AxesSubplot at 0x2353f310e08>
In [104]:
plt.scatter(y_test , y_pred_model5)
Out[104]:
<matplotlib.collections.PathCollection at 0x23540f0a408>
In [105]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model5))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model5))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model5)))
MAE: 162.98927180254597
MSE: 60272.36069438864
RMSE: 245.50429872894006
In [106]:
from sklearn.metrics import r2_score

y_pred = y_pred_model5
y_test = y_test
model = 'model5 Decision Tree Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [107]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model5.mean(),
                                             'Median of AbsErrors' : abs_err_model5.median(),
                                             'SD of AbsErrors' :     abs_err_model5.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model5),
                                             'Min of AbsErrors':     abs_err_model5.min(),
                                             'Max of AbsErrors':     abs_err_model5.max()}, index = ['Model5: Decision Tree Regression']), 
                               ignore_index = False)

model_comp
Out[107]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
Model5: Decision Tree Regression 162.989272 78.558773 185.351198 223.772135 0.769051 827.083624

Model6: Bagging

In [109]:
from sklearn.ensemble import BaggingRegressor
model6 = BaggingRegressor(n_estimators = 500, oob_score = True)
model6.fit(X_train, logy_train)
y_pred_model6 = model6.predict(X_test)
y_pred_model6 = np.exp(y_pred_model6)
abs_err_model6 = np.abs(y_pred_model6 - y_test)
In [110]:
sns.distplot(y_test - y_pred_model6)
Out[110]:
<matplotlib.axes._subplots.AxesSubplot at 0x2353f4ff208>
In [111]:
plt.scatter(y_test , y_pred_model6)
Out[111]:
<matplotlib.collections.PathCollection at 0x23540a2e088>
In [112]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model6))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model6))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model6)))
MAE: 110.54863249556075
MSE: 30671.64508166156
RMSE: 175.13322095382577
In [113]:
from sklearn.metrics import r2_score

y_pred = y_pred_model6
y_test = y_test
model = 'model6 Bagging Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [114]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model6.mean(),
                                             'Median of AbsErrors' : abs_err_model6.median(),
                                             'SD of AbsErrors' :     abs_err_model6.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model6),
                                             'Min of AbsErrors':     abs_err_model6.min(),
                                             'Max of AbsErrors':     abs_err_model6.max()}, index = ['Model6: Bagging Regression']), 
                               ignore_index = False)

model_comp
Out[114]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
Model5: Decision Tree Regression 162.989272 78.558773 185.351198 223.772135 0.769051 827.083624
Model6: Bagging Regression 110.548632 58.805452 137.133019 153.685308 1.442460 747.780147

Model7: Random Forest

In [118]:
from sklearn.ensemble import RandomForestRegressor
model7 = RandomForestRegressor(n_estimators = 246,
                               oob_score = True, 
                               max_features = 'sqrt', 
                               max_depth = 26, 
                               min_samples_split = 20, 
                               min_samples_leaf = 1)

model7.fit(X_train, logy_train)
y_pred_model7 = model7.predict(X_test)
y_pred_model7 = np.exp(y_pred_model7)
abs_err_model7 = np.abs(y_pred_model7 - y_test)
In [117]:
from sklearn.model_selection import RandomizedSearchCV
n_estimators = [int(x) for x in np.linspace(start = 100, stop = 2000, num = 40)]
max_features = ['auto', 'sqrt']
max_depth = [int(x) for x in np.linspace(5, 40, num = 6)]
min_samples_split = [2, 5, 10, 15, 20,25,30,35,40,100]
min_samples_leaf = [1, 2, 5, 10]

random_grid = {'n_estimators': n_estimators,
               'max_features': max_features,
               'max_depth': max_depth,
               'min_samples_split': min_samples_split,
               'min_samples_leaf': min_samples_leaf}

rf_random = RandomizedSearchCV(estimator = model7, 
                               param_distributions = random_grid, 
                               scoring='neg_mean_squared_error',
                               n_iter = 10, 
                               cv = 5, 
                               verbose=2, 
                               random_state=42, 
                               n_jobs = 1)

rf_random.fit(X_train, logy_train)
rf_random.best_params_
Fitting 5 folds for each of 10 candidates, totalling 50 fits
[CV] n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33 
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[CV]  n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33, total=   3.0s
[CV] n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33 
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    2.9s remaining:    0.0s
[CV]  n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33, total=   3.0s
[CV] n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33, total=   3.4s
[CV] n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33, total=   3.1s
[CV] n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1805, min_samples_split=20, min_samples_leaf=10, max_features=sqrt, max_depth=33, total=   3.3s
[CV] n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5 
[CV]  n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5, total=   2.4s
[CV] n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5 
[CV]  n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5, total=   2.3s
[CV] n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5 
[CV]  n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5, total=   2.3s
[CV] n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5 
[CV]  n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5, total=   2.5s
[CV] n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5 
[CV]  n_estimators=1074, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=5, total=   2.3s
[CV] n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12, total=   2.8s
[CV] n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12, total=   3.2s
[CV] n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12, total=   2.9s
[CV] n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12, total=   2.7s
[CV] n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1561, min_samples_split=20, min_samples_leaf=2, max_features=sqrt, max_depth=12, total=   2.5s
[CV] n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26, total=   0.4s
[CV] n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26, total=   0.4s
[CV] n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26, total=   0.4s
[CV] n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26, total=   0.4s
[CV] n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=100, min_samples_leaf=2, max_features=sqrt, max_depth=26, total=   0.4s
[CV] n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.5s
[CV] n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.5s
[CV] n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.5s
[CV] n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.5s
[CV] n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=294, min_samples_split=10, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.5s
[CV] n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12, total=   2.0s
[CV] n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12, total=   2.0s
[CV] n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12, total=   2.1s
[CV] n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12, total=   2.0s
[CV] n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12 
[CV]  n_estimators=1317, min_samples_split=30, min_samples_leaf=10, max_features=sqrt, max_depth=12, total=   2.0s
[CV] n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40 
[CV]  n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40, total=   1.2s
[CV] n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40 
[CV]  n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40, total=   1.4s
[CV] n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40 
[CV]  n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40, total=   1.4s
[CV] n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40 
[CV]  n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40, total=   1.4s
[CV] n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40 
[CV]  n_estimators=587, min_samples_split=5, min_samples_leaf=5, max_features=auto, max_depth=40, total=   1.4s
[CV] n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12 
[CV]  n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12, total=   3.2s
[CV] n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12 
[CV]  n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12, total=   2.8s
[CV] n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12 
[CV]  n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12, total=   2.5s
[CV] n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12 
[CV]  n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12, total=   2.5s
[CV] n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12 
[CV]  n_estimators=1366, min_samples_split=2, min_samples_leaf=10, max_features=auto, max_depth=12, total=   2.5s
[CV] n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33, total=   2.3s
[CV] n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33, total=   2.2s
[CV] n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33, total=   2.2s
[CV] n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33, total=   2.2s
[CV] n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33 
[CV]  n_estimators=1220, min_samples_split=2, min_samples_leaf=1, max_features=sqrt, max_depth=33, total=   2.1s
[CV] n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.4s
[CV] n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.4s
[CV] n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.5s
[CV] n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.5s
[CV] n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26 
[CV]  n_estimators=246, min_samples_split=20, min_samples_leaf=1, max_features=sqrt, max_depth=26, total=   0.4s
[Parallel(n_jobs=1)]: Done  50 out of  50 | elapsed:  1.5min finished
Out[117]:
{'n_estimators': 246,
 'min_samples_split': 20,
 'min_samples_leaf': 1,
 'max_features': 'sqrt',
 'max_depth': 26}
In [120]:
sns.distplot(y_test - y_pred_model7)
Out[120]:
<matplotlib.axes._subplots.AxesSubplot at 0x2353f271a88>
In [121]:
plt.scatter(y_test , y_pred_model7)
Out[121]:
<matplotlib.collections.PathCollection at 0x23540ce8ec8>
In [122]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model7))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model7))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model7)))
MAE: 115.34020989850781
MSE: 31939.059849376987
RMSE: 178.71502412885434
In [123]:
from sklearn.metrics import r2_score

y_pred = y_pred_model7
y_test = y_test
model = 'model7 Random Forest Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [124]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model7.mean(),
                                             'Median of AbsErrors' : abs_err_model7.median(),
                                             'SD of AbsErrors' :     abs_err_model7.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model7),
                                             'Min of AbsErrors':     abs_err_model7.min(),
                                             'Max of AbsErrors':     abs_err_model7.max()}, index = ['Model7: Random Forest Regression']), 
                               ignore_index = False)

model_comp
Out[124]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
Model5: Decision Tree Regression 162.989272 78.558773 185.351198 223.772135 0.769051 827.083624
Model6: Bagging Regression 110.548632 58.805452 137.133019 153.685308 1.442460 747.780147
Model7: Random Forest Regression 115.340210 58.109284 137.818992 160.515046 3.225445 745.132697

Model8: Gradient Boost Regression

In [ ]:
{'subsample': 1,
 'n_estimators': 1000,
 'min_samples_leaf': 3,
 'max_depth': 6,
 'learning_rate': 0.2}
In [128]:
from sklearn.ensemble import GradientBoostingRegressor
model8 = GradientBoostingRegressor(learning_rate = 0.2, 
                                   max_depth = 6, 
                                   min_samples_leaf = 3, 
                                   n_estimators = 1000, 
                                   subsample = 1)

model8.fit(X_train, logy_train)
y_pred_model8 = model8.predict(X_test)
y_pred_model8 = np.exp(y_pred_model8)
abs_err_model8 = np.abs(y_pred_model8 - y_test)
In [127]:
from sklearn.model_selection import RandomizedSearchCV

learning_rate = [0.01,0.1, 0.2, 0.3, 0.4, 0.5]
n_estimators = [500, 600, 700, 800, 900, 1000, 1100, 1200]
subsample = [1, 2, 3, 4]
max_depth = [2, 3, 4, 5, 6, 7]
min_samples_leaf = [3, 4, 5, 6, 7, 8]


random_grid = {'n_estimators': n_estimators,
               'max_depth': max_depth,
               'min_samples_leaf': min_samples_leaf, 
               'learning_rate':learning_rate, 
                'subsample': subsample}

rf_random = RandomizedSearchCV(estimator = model8, 
                               param_distributions = random_grid, 
                               scoring='neg_mean_squared_error', 
                               n_iter = 10, 
                               cv = 5, 
                               verbose=2, 
                               random_state=42, 
                               n_jobs = 1)

rf_random.fit(X_train, logy_train)
rf_random.best_params_
Fitting 5 folds for each of 10 candidates, totalling 50 fits
[CV] subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01 
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01, total=   1.7s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01 
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    1.6s remaining:    0.0s
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01, total=   1.6s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01 
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01, total=   1.5s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01 
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01, total=   1.4s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01 
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=5, max_depth=6, learning_rate=0.01, total=   1.4s
[CV] subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4 
[CV]  subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4 
[CV]  subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4 
[CV]  subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4 
[CV]  subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4 
[CV]  subsample=3, n_estimators=800, min_samples_leaf=3, max_depth=6, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=700, min_samples_leaf=4, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4 
[CV]  subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4 
[CV]  subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4 
[CV]  subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4 
[CV]  subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4 
[CV]  subsample=4, n_estimators=600, min_samples_leaf=3, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3 
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 4

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 4

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 4

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 4

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 4

  FitFailedWarning)
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3, total=   0.5s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3 
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3, total=   0.4s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3 
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3, total=   0.4s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3 
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3, total=   0.4s
[CV] subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3 
[CV]  subsample=1, n_estimators=1200, min_samples_leaf=6, max_depth=3, learning_rate=0.3, total=   0.4s
[CV] subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2 
[CV]  subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2, total=   0.4s
[CV] subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2 
[CV]  subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2, total=   0.4s
[CV] subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2 
[CV]  subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2, total=   0.4s
[CV] subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2 
[CV]  subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2, total=   0.3s
[CV] subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2 
[CV]  subsample=1, n_estimators=1000, min_samples_leaf=3, max_depth=6, learning_rate=0.2, total=   0.4s
[CV] subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4 
[CV]  subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4 
[CV]  subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4 
[CV]  subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4 
[CV]  subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4 
[CV]  subsample=3, n_estimators=600, min_samples_leaf=8, max_depth=7, learning_rate=0.4, total=   0.0s
[CV] subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5 
[CV]  subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5, total=   0.0s
[CV] subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5 
[CV]  subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5, total=   0.0s
[CV] subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5 
[CV]  subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5, total=   0.0s
[CV] subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5 
[CV]  subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5, total=   0.0s
[CV] subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5 
[CV]  subsample=2, n_estimators=1100, min_samples_leaf=6, max_depth=4, learning_rate=0.5, total=   0.0s
[CV] subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01 
[CV]  subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01, total=   0.0s
[CV] subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01 
[CV]  subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01, total=   0.0s
[CV] subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01 
[CV]  subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01, total=   0.0s
[CV] subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01 
[CV]  subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01, total=   0.0s
[CV] subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01 
[CV]  subsample=3, n_estimators=900, min_samples_leaf=5, max_depth=4, learning_rate=0.01, total=   0.0s
[CV] subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4, total=   0.0s
[CV] subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4 
[CV]  subsample=3, n_estimators=1000, min_samples_leaf=7, max_depth=5, learning_rate=0.4, total=   0.0s
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 2

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 2

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 2

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 2

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 2

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:536: FitFailedWarning: Estimator fit failed. The score on this train-test partition for these parameters will be set to nan. Details: 
ValueError: subsample must be in (0,1] but was 3

  FitFailedWarning)
[Parallel(n_jobs=1)]: Done  50 out of  50 | elapsed:   11.8s finished
Out[127]:
{'subsample': 1,
 'n_estimators': 1000,
 'min_samples_leaf': 3,
 'max_depth': 6,
 'learning_rate': 0.2}
In [129]:
sns.distplot(y_test - y_pred_model8)
Out[129]:
<matplotlib.axes._subplots.AxesSubplot at 0x23541171f88>
In [130]:
plt.scatter(y_test , y_pred_model8)
Out[130]:
<matplotlib.collections.PathCollection at 0x2353f5442c8>
In [131]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model8))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model8))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model8)))
MAE: 126.72254202286322
MSE: 34419.81162336832
RMSE: 185.52577077960981
In [132]:
from sklearn.metrics import r2_score

y_pred = y_pred_model8
y_test = y_test
model = 'model8 Gradient Boost Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [133]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model8.mean(),
                                             'Median of AbsErrors' : abs_err_model8.median(),
                                             'SD of AbsErrors' :     abs_err_model8.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model8),
                                             'Min of AbsErrors':     abs_err_model8.min(),
                                             'Max of AbsErrors':     abs_err_model8.max()}, index = ['Model8: Gradient Boost Regression']), 
                               ignore_index = False)

model_comp
Out[133]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
Model5: Decision Tree Regression 162.989272 78.558773 185.351198 223.772135 0.769051 827.083624
Model6: Bagging Regression 110.548632 58.805452 137.133019 153.685308 1.442460 747.780147
Model7: Random Forest Regression 115.340210 58.109284 137.818992 160.515046 3.225445 745.132697
Model8: Gradient Boost Regression 126.722542 69.261401 136.800253 106.438768 3.763734 532.900731

Model9: XGBoost

In [135]:
from xgboost import XGBRegressor
from scipy.stats import uniform, randint
In [ ]:
{'gamma': 0.19993048585762774,
 'learning_rate': 0.04399969896408463,
 'max_depth': 5,
 'n_estimators': 115,
 'subsample': 0.6931085361721216}
In [167]:
model9 = XGBRegressor(gamma = 0.19993048585762774, 
                      learning_rate = 0.04399969896408463, 
                      max_depth = 5, 
                      n_estimators = 115, 
                      subsample = 0.6931085361721216, 
                      colsample_bytree = 0.39, 
                      reg_alpha = 0.07, 
                      reg_lambda = 0.055)
model9.fit(X_train, logy_train)
y_pred_model9 = model9.predict(X_test)
y_pred_model9 = np.exp(y_pred_model9)
abs_err_model9 = np.abs(y_pred_model9 - y_test)
In [166]:
params = {
    "gamma": uniform(0, 0.5),
    "learning_rate": uniform(0.03, 0.3), # default 0.1 
    "max_depth": randint(2, 6), # default 3
    "n_estimators": randint(100, 150), # default 100
    "subsample": uniform(0.6, 0.4)
}

xgb = RandomizedSearchCV(estimator = model9, 
                         param_distributions = params,
                         scoring='neg_mean_squared_error',
                         n_iter = 10, 
                         cv = 5, 
                         verbose=2, 
                         random_state=42, 
                         n_jobs = 1)

xgb.fit(X_train, logy_train)
xgb.best_params_
Fitting 5 folds for each of 10 candidates, totalling 50 fits
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.1s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.1s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.1s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.1s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.1s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.1s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.1s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.1s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.1s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.1s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.1s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.1s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.1s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.1s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.1s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.1s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.1s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.1s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.1s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.1s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.1s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.1s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.1s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.1s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.1s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.1s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.1s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.1s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.1s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.1s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.1s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.1s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.1s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.1s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.1s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.1s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.1s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.1s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.1s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.1s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.1s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.1s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.1s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.1s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.1s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.1s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.1s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.1s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.1s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.1s
[Parallel(n_jobs=1)]: Done  50 out of  50 | elapsed:    5.0s finished
Out[166]:
{'gamma': 0.19993048585762774,
 'learning_rate': 0.04399969896408463,
 'max_depth': 5,
 'n_estimators': 115,
 'subsample': 0.6931085361721216}
In [168]:
sns.distplot(y_test - y_pred_model9)
Out[168]:
<matplotlib.axes._subplots.AxesSubplot at 0x2353eac5f48>
In [169]:
plt.scatter(y_test , y_pred_model9)
Out[169]:
<matplotlib.collections.PathCollection at 0x235439ad6c8>
In [170]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model9))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model9))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model9)))
MAE: 111.02415132342644
MSE: 29909.376834659353
RMSE: 172.94327634996208
In [171]:
from sklearn.metrics import r2_score

y_pred = y_pred_model9
y_test = y_test
model = 'model9 XGradient Boost Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [175]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model9.mean(),
                                             'Median of AbsErrors' : abs_err_model9.median(),
                                             'SD of AbsErrors' :     abs_err_model9.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model9),
                                             'Min of AbsErrors':     abs_err_model9.min(),
                                             'Max of AbsErrors':     abs_err_model9.max()}, index = ['Model9: XGradient Boost Regression']), 
                               ignore_index = False)

model_comp
Out[175]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
Model5: Decision Tree Regression 162.989272 78.558773 185.351198 223.772135 0.769051 827.083624
Model6: Bagging Regression 110.548632 58.805452 137.133019 153.685308 1.442460 747.780147
Model7: Random Forest Regression 115.340210 58.109284 137.818992 160.515046 3.225445 745.132697
Model8: Gradient Boost Regression 126.722542 69.261401 136.800253 106.438768 3.763734 532.900731
Model9: XGradient Boost Regression 111.024151 53.490540 133.869898 149.096519 0.053513 774.368569

Model10: CatBoost

In [178]:
from catboost import CatBoostRegressor
model10 = CatBoostRegressor(learning_rate = 0.03, 
                            l2_leaf_reg = 5, 
                            depth = 10)
model10.fit(X_train, logy_train)
y_pred_model10 = model10.predict(X_test)
y_pred_model10 = np.exp(y_pred_model10)
abs_err_model10 = np.abs(y_pred_model10 - y_test)
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In [177]:
grid = {'learning_rate': [0.03, 0.1],
        'depth': [4, 6, 10],
        'l2_leaf_reg': [1, 3, 5, 7, 9]}

cb = RandomizedSearchCV(estimator = model10, 
                        param_distributions = grid,
                        scoring='neg_mean_squared_error',
                        n_iter = 10, 
                        cv = 5, 
                        verbose=2, 
                        random_state=42, 
                        n_jobs = 1)

cb.fit(X_train,logy_train)
cb.best_params_
Fitting 5 folds for each of 10 candidates, totalling 50 fits
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=10 ......................
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[CV] ....... learning_rate=0.1, l2_leaf_reg=7, depth=10, total=  32.3s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=7, depth=10, total=  32.5s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=7, depth=10, total=  31.3s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=7, depth=10, total=  32.3s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=7, depth=10, total=  32.6s
[CV] learning_rate=0.1, l2_leaf_reg=5, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=5, depth=6, total=   2.8s
[CV] learning_rate=0.1, l2_leaf_reg=5, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=5, depth=6, total=   3.0s
[CV] learning_rate=0.1, l2_leaf_reg=5, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=5, depth=6, total=   2.8s
[CV] learning_rate=0.1, l2_leaf_reg=5, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=5, depth=6, total=   2.6s
[CV] learning_rate=0.1, l2_leaf_reg=5, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=5, depth=6, total=   2.7s
[CV] learning_rate=0.1, l2_leaf_reg=3, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=3, depth=10, total=  30.3s
[CV] learning_rate=0.1, l2_leaf_reg=3, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=3, depth=10, total=  30.8s
[CV] learning_rate=0.1, l2_leaf_reg=3, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=3, depth=10, total=  30.6s
[CV] learning_rate=0.1, l2_leaf_reg=3, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=3, depth=10, total=  31.3s
[CV] learning_rate=0.1, l2_leaf_reg=3, depth=10 ......................
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[CV] ....... learning_rate=0.1, l2_leaf_reg=3, depth=10, total=  31.9s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=7, depth=6, total=   2.7s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=7, depth=6, total=   2.6s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=7, depth=6, total=   2.7s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=7, depth=6, total=   2.7s
[CV] learning_rate=0.1, l2_leaf_reg=7, depth=6 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=7, depth=6, total=   2.7s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=9, depth=4, total=   1.7s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=9, depth=4, total=   1.7s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=9, depth=4, total=   1.9s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=9, depth=4, total=   1.8s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=9, depth=4, total=   1.8s
[CV] learning_rate=0.1, l2_leaf_reg=9, depth=4 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=9, depth=4, total=   1.7s
[CV] learning_rate=0.1, l2_leaf_reg=9, depth=4 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=9, depth=4, total=   1.7s
[CV] learning_rate=0.1, l2_leaf_reg=9, depth=4 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=9, depth=4, total=   1.7s
[CV] learning_rate=0.1, l2_leaf_reg=9, depth=4 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=9, depth=4, total=   1.8s
[CV] learning_rate=0.1, l2_leaf_reg=9, depth=4 .......................
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[CV] ........ learning_rate=0.1, l2_leaf_reg=9, depth=4, total=   1.6s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=9, depth=10, total=  37.6s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=9, depth=10, total=  39.2s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=9, depth=10, total=  33.5s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=9, depth=10, total=  37.2s
[CV] learning_rate=0.03, l2_leaf_reg=9, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=9, depth=10, total=  35.1s
[CV] learning_rate=0.03, l2_leaf_reg=5, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=5, depth=10, total=  38.5s
[CV] learning_rate=0.03, l2_leaf_reg=5, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=5, depth=10, total=  34.0s
[CV] learning_rate=0.03, l2_leaf_reg=5, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=5, depth=10, total=  37.7s
[CV] learning_rate=0.03, l2_leaf_reg=5, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=5, depth=10, total=  36.8s
[CV] learning_rate=0.03, l2_leaf_reg=5, depth=10 .....................
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[CV] ...... learning_rate=0.03, l2_leaf_reg=5, depth=10, total=  39.0s
[CV] learning_rate=0.03, l2_leaf_reg=3, depth=6 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=3, depth=6, total=   3.2s
[CV] learning_rate=0.03, l2_leaf_reg=3, depth=6 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=3, depth=6, total=   3.5s
[CV] learning_rate=0.03, l2_leaf_reg=3, depth=6 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=3, depth=6, total=   3.7s
[CV] learning_rate=0.03, l2_leaf_reg=3, depth=6 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=3, depth=6, total=   3.2s
[CV] learning_rate=0.03, l2_leaf_reg=3, depth=6 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=3, depth=6, total=   2.9s
[CV] learning_rate=0.03, l2_leaf_reg=1, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=1, depth=4, total=   1.6s
[CV] learning_rate=0.03, l2_leaf_reg=1, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=1, depth=4, total=   1.8s
[CV] learning_rate=0.03, l2_leaf_reg=1, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=1, depth=4, total=   1.8s
[CV] learning_rate=0.03, l2_leaf_reg=1, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=1, depth=4, total=   1.7s
[CV] learning_rate=0.03, l2_leaf_reg=1, depth=4 ......................
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[CV] ....... learning_rate=0.03, l2_leaf_reg=1, depth=4, total=   1.6s
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Out[177]:
{'learning_rate': 0.03, 'l2_leaf_reg': 5, 'depth': 10}
In [179]:
sns.distplot(y_test - y_pred_model10)
Out[179]:
<matplotlib.axes._subplots.AxesSubplot at 0x235411db508>
In [180]:
plt.scatter(y_test , y_pred_model10)
Out[180]:
<matplotlib.collections.PathCollection at 0x2354098a3c8>
In [181]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model10))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model10))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model10)))
MAE: 124.36481600298288
MSE: 28645.260923268437
RMSE: 169.2491090767347
In [182]:
from sklearn.metrics import r2_score

y_pred = y_pred_model10
y_test = y_test
model = 'model10 CatBoost Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [198]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model10.mean(),
                                             'Median of AbsErrors' : abs_err_model10.median(),
                                             'SD of AbsErrors' :     abs_err_model10.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model10),
                                             'Min of AbsErrors':     abs_err_model10.min(),
                                             'Max of AbsErrors':     abs_err_model10.max()}, index = ['Model10: CatBoost Regression']), 
                               ignore_index = False)

model_comp
Out[198]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
Model5: Decision Tree Regression 162.989272 78.558773 185.351198 223.772135 0.769051 827.083624
Model6: Bagging Regression 110.548632 58.805452 137.133019 153.685308 1.442460 747.780147
Model7: Random Forest Regression 115.340210 58.109284 137.818992 160.515046 3.225445 745.132697
Model8: Gradient Boost Regression 126.722542 69.261401 136.800253 106.438768 3.763734 532.900731
Model9: XGradient Boost Regression 111.024151 53.490540 133.869898 149.096519 0.053513 774.368569
Model10: CatBoost Regression 124.364816 97.575426 115.896890 123.215817 3.237146 562.148719

Model11: LightBoost

In [ ]:
{'gamma': 0.22007624686980065,
 'learning_rate': 0.06661147045343364,
 'max_depth': 2,
 'n_estimators': 107,
 'subsample': 0.6137554084460873}
In [186]:
from lightgbm import LGBMRegressor
model11 = LGBMRegressor(gamma = 0.22007624686980065,
                        learning_rate = 0.06661147045343364,
                        max_depth = 2, 
                        n_estimators = 107, 
                        subsample = 0.6137554084460873)
model11.fit(X_train, logy_train)
y_pred_model11 = model11.predict(X_test)
y_pred_model11 = np.exp(y_pred_model11)
abs_err_model11 = np.abs(y_pred_model11 - y_test)
In [185]:
params = {
    "gamma": uniform(0, 0.5),
    "learning_rate": uniform(0.03, 0.3), # default 0.1 
    "max_depth": randint(2, 6), # default 3
    "n_estimators": randint(100, 150), # default 100
    "subsample": uniform(0.6, 0.4)
}

lb = RandomizedSearchCV(estimator = model11, 
                        param_distributions = params,
                        scoring='neg_mean_squared_error',
                        n_iter = 10, 
                        cv = 5, 
                        verbose=2, 
                        random_state=42, 
                        n_jobs = 1)
lb.fit(X_train, logy_train)
lb.best_params_
Fitting 5 folds for each of 10 candidates, totalling 50 fits
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[LightGBM] [Warning] Unknown parameter: gamma
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.3s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.0s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[LightGBM] [Warning] Unknown parameter: gamma
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.2s remaining:    0.0s
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.0s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.0s
[CV] gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.18727005942368125, learning_rate=0.3152142919229748, max_depth=4, n_estimators=107, subsample=0.8394633936788146, total=   0.0s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.0s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.0s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.0s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.0s
[CV] gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.07800932022121826, learning_rate=0.07679835610086079, max_depth=4, n_estimators=110, subsample=0.9464704583099741, total=   0.0s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.0s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.0s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.0s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.0s
[CV] gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.3005575058716044, learning_rate=0.24242177333881365, max_depth=3, n_estimators=101, subsample=0.8887995089067299, total=   0.0s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.0s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.1s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.1s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.0s
[CV] gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.4692763545078751, learning_rate=0.030233629752304297, max_depth=5, n_estimators=120, subsample=0.8469926038510867, total=   0.0s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.0s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.0s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.0s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.0s
[CV] gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.30582658024414044, learning_rate=0.03211989156591522, max_depth=2, n_estimators=148, subsample=0.8099098641033556, total=   0.0s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.1s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.0s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.0s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.0s
[CV] gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.19993048585762774, learning_rate=0.04399969896408463, max_depth=5, n_estimators=115, subsample=0.6931085361721216, total=   0.0s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.0s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.0s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.0s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.0s
[CV] gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.0453032172664104, learning_rate=0.2155158027999262, max_depth=5, n_estimators=102, subsample=0.9439761626945282, total=   0.0s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.0s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.0s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.0s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.0s
[CV] gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.34015376929388985, learning_rate=0.16514977559086289, max_depth=3, n_estimators=103, subsample=0.9768807022739411, total=   0.0s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.0s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.0s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.0s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.0s
[CV] gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.28164410892276964, learning_rate=0.14562495076197482, max_depth=3, n_estimators=101, subsample=0.8736932106048627, total=   0.0s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.0s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.0s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.0s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.0s
[CV] gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873 
[LightGBM] [Warning] Unknown parameter: gamma
[CV]  gamma=0.22007624686980065, learning_rate=0.06661147045343364, max_depth=2, n_estimators=107, subsample=0.6137554084460873, total=   0.0s
[LightGBM] [Warning] Unknown parameter: gamma
[Parallel(n_jobs=1)]: Done  50 out of  50 | elapsed:    2.4s finished
Out[185]:
{'gamma': 0.22007624686980065,
 'learning_rate': 0.06661147045343364,
 'max_depth': 2,
 'n_estimators': 107,
 'subsample': 0.6137554084460873}
In [187]:
sns.distplot(y_test - y_pred_model11)
Out[187]:
<matplotlib.axes._subplots.AxesSubplot at 0x2354796ecc8>
In [188]:
plt.scatter(y_test , y_pred_model11)
Out[188]:
<matplotlib.collections.PathCollection at 0x2353f28b988>
In [189]:
print('MAE:', metrics.mean_absolute_error(y_test, y_pred_model11))
print('MSE:', metrics.mean_squared_error(y_test, y_pred_model11))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, y_pred_model11)))
MAE: 124.93325779962663
MSE: 41085.0395500319
RMSE: 202.69444874004787
In [190]:
from sklearn.metrics import r2_score

y_pred = y_pred_model11
y_test = y_test
model = 'model11 LightBoost Regression'

plt.figure(figsize=(15, 15), dpi = 150);
plt.subplots_adjust(hspace = 0.25, wspace = 0.25);

plt.subplots(figsize=(16,6));
plt.scatter(x = y_test, y = y_pred, color = 'blue');
#Add 45 degree line
xp = np.linspace(y_test.min(), y_test.max(), 100)
plt.plot(xp, xp, 'k', alpha = 0.9, linewidth = 2, color = 'red')
plt.xlabel('Actual Value');
plt.ylabel('Predicted Value');

plt.title(f'{model}');
plt.subplots(figsize=(17,6));

x_points = list(range(len(y_test)));
plt.plot(x_points, y_test, label='y_real', color = 'blue');
plt.plot(x_points, y_pred, label='y_predict', color = 'red');
plt.legend();
plt.grid()
plt.title(f'{model}');
plt.show();
<Figure size 2250x2250 with 0 Axes>
In [199]:
model_comp = model_comp.append(pd.DataFrame({'Mean of AbsErrors':    abs_err_model11.mean(),
                                             'Median of AbsErrors' : abs_err_model11.median(),
                                             'SD of AbsErrors' :     abs_err_model11.std(),
                                             'IQR of AbsErrors':     iqr(abs_err_model11),
                                             'Min of AbsErrors':     abs_err_model11.min(),
                                             'Max of AbsErrors':     abs_err_model11.max()}, index = ['Model11: LightBoost Regression']), 
                               ignore_index = False)

model_comp
Out[199]:
Mean of AbsErrors Median of AbsErrors SD of AbsErrors IQR of AbsErrors Min of AbsErrors Max of AbsErrors
Model1: Linear-Ragression 223.148958 158.574170 198.785517 216.725217 3.569232 1047.957143
Model2: Ridge Regression 226.441674 151.029550 293.532084 136.707544 7.679097 1897.768941
Model3: Lasso Regression 235.833326 142.116905 324.730397 156.625954 3.744212 2181.596147
Model4: KNN Regression 160.407478 81.167175 190.775927 226.393202 2.543116 837.841616
Model5: Decision Tree Regression 162.989272 78.558773 185.351198 223.772135 0.769051 827.083624
Model6: Bagging Regression 110.548632 58.805452 137.133019 153.685308 1.442460 747.780147
Model7: Random Forest Regression 115.340210 58.109284 137.818992 160.515046 3.225445 745.132697
Model8: Gradient Boost Regression 126.722542 69.261401 136.800253 106.438768 3.763734 532.900731
Model9: XGradient Boost Regression 111.024151 53.490540 133.869898 149.096519 0.053513 774.368569
Model10: CatBoost Regression 124.364816 97.575426 115.896890 123.215817 3.237146 562.148719
Model11: LightBoost Regression 124.933258 71.528389 161.141731 136.835531 5.743488 849.233318
In [ ]:
http://www.science.smith.edu/~jcrouser/SDS293/labs/lab11-py.html